Question 612544: Britney has 30 coins, all nickels (5 cents) and dimes (10 cents). If the nickels were changed to quarters (25 cents) and the dimes changed to nickels, the total value of the coins would remain unchanged. How many nickels and how many dimes does she have?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Britney has 30 coins, all nickels (5 cents) and dimes (10 cents).
If the nickels were changed to quarters (25 cents) and the dimes changed to nickels, the total value of the coins would remain unchanged.
How many nickels and how many dimes does she have?
:
Let n = no. of nickels
Let d = no. of dimes
:
Write an equation for each statement:
:
"Britney has 30 coins, all nickels (5 cents) and dimes (10 cents)."
n + d = 30
n = (30-d)
:
"If the nickels were changed to quarters (25 cents) and the dimes changed to nickels, the total value of the coins would remain unchanged.'
.05n + .10d = .25n + .05d
.10d - .05d = .25n - .05n
.05d = .20n
get rid of those decimals, mult by 100
5d = 20n
divide by 5
d = 4n
replace n with (30-d)
d = 4(30-d)
d = 120 - 4d
d + 4d = 120
5d = 120
d = 120/5
d = 24 dimes
then
30 - 24 = 6 nickels
:
:
Check solutions in the statement:
" the nickels were changed to quarters (25 cents) and the dimes changed to nickels, the total value of the coins would remain unchanged.
.05(6) + .10(24) = .25(6) + .05(24)
.30 + 2.40 = 1.50 + 1.20
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